Alexei V. POGORELOV
POGORELOV Aleksey Vasilevich is the outstandig mathematician of our country, the scientist renowned throughout the world, the academician of Academy of Sciences of Russia and Ukraine, the Honoured Scientist of Ukraine.
A.V. Pogorelov was born in 1919, March 3, in Korocha of Belgorod district (Russia). He graduated Kharkov University (1941) and N.E. Zhukowsky Air Force Academy (1945). His professional experience advanced from engineer-designer at TsAGI (1945). At the same time he attended the external post-graduate courses. A.V. Pogorelov defended the Candidate's thesis (1947) and the Doctor's thesis (1948). He was elected Corresponding Member of UkrSSR Academy of Sciences (1951), Corresponding Member of USSR Academy of Sciences and Academician of UkrSSR Academy of Sciences (1960). Since 1976, he is the Academician of USSR Academy of Sciences. He headed (i) the Chair of Geometry at Kharkov State University (1950-1959), (ii) Geometry Department of Institute of Mathematics at Kharkov State University (1947-1950), (iii) Geometry Department of Institute of Mathematics of Academy of Sciences of Ukraine (1959-1960) and (iv) Geometry Department at B.Verkin Institute for Low Temperature Physics&Engineering, Academy of Sciences of Ukraine (1960 up to now).
The scope of his scientific interests is defined by a rare combination of gifts for mathematics and engineering. The studies made by A.V Pogorelov are concerned with geometry in the large, fundamentals of geometry, theory of partial differential equations, theory of stability of thin shells, cryogenic electric mashine engineering. They were generally recognized when he solved the very difficult problem of rigidity of general convex surfaces by their metrics. The theorem proved by A.V. Pogorelov includes the well- known A. Cachy, H. Liebmann, S. Cohn-Vossen results as partial cases. Subsequently,he also obtained a number of fundamental results: proved that a convex surface with a regular metrics is also regular, solved the generalized Weyl problem on isometric immersion of a Riemannian manifold homeomorphic to the sphere in the Riemannian 3-dimensional space, the problem of infinitesimal bendings of general convex surfaces, the Dirichlet problem for multidimensional Monge-Ampere equation of elliptic type, obtained a regular solution of the Minkowsky multidimensional problem and a complete solution of the Hilbert's fourth problem.
A.V. Pogorelov has developed the original geometrical theory of stability of elastic shells and determined a series of new results on value of the critical loads, which was corroborated by himself experimentally. He also suggested original solution in the field of the superconducting electric mashine engineering. A.V. Pogorelov is the author of the textbooks written for higher schools on all basic geometrical subjects which are notable for treir original text, mathematical strict proof and clarity.His attention has been also concentrated on t he improvement of the school mathematical education. He created the text book of geometry which was included into school curricula in 1982 after being experimentally tested in a number of secondary schools. The textbook is noted for its practical aspect of teaching geometry, from one part, and direction of attention towards a development of logical thinking, abilities of pupils according to their age features and individual gifts, on the other part, that fully meets up-to-date requirements.
A.V. Pogorelov is an author of more than 200 publications including about 40 monographies and textbooks. Nierly all his monographies were translated into other languages abroad.
His achievements in the scientific researches were appraised at their true worth and A.V. Pogorelov was awarded Lenin Prize (1962), USSR State Prize (1950), Ukraine State Prize (1973), International Lobachewsky Prize (1959) and Krylov Prize of Academy of Sciences of Ukraine (1988). For his scientific and pedagogica activity A.V. Pogorelov was decorated with two Lenin orders, order of the Red Banner of Labour and Diploma of Presidium of the Supreme Soviet of Ukraine. For the textbook of geometry written by A.V. Pogorelov for secondary schools he also received the title "Excellent Teacher of USSR" and was rewarded with a A.S. Makarenko medal.
A.V. Pogorelov's monographies.
. Die eindeutige Bestimmung allgemeiner convexer Flachen(in German).- Berlin: Akad. Verl., 1956.- 79 s.
2. Die Verbiegung konvexer Flachen (in German).- Berlin: Akad. Verl., 1957.- 135 s.
3. Surfaces of bounded extrinsic curvature (in Russian).-Kharkov: Universitetizdat, 1956.- 128 p.
4. Einige Untersuchungen zur Riemannschen Geometrie "im Grossen" (in German).- Berlin : VEB Deutch. Verl. Wiss., 1960.- 71 p.
5. Infinitesimal bending of general convex surfaces(in Russian).- Kharkov: Universitetizdat, 1959.- 106 p.
6. To the theory of convex elastic shells in postcritical stage (in Russian).- Kharkov : Universitetizdat, 1960.- 78 p.
7. On Monge-Ampere equations of elliptic type (in Russian) .-Kharkov: Universitetizdat,1964.- 114 p.
8. Topic in the theory of surfaces in elliptic space(in English). - New-York : Gordon&Breach, 1961.-130 p.
9. Some results on surfaces theory in the large (in English). Advances math., 1964, 1, N 2., p. 191-264.
10. Cylindrical shells under postcritical deformations(in Russian)
I. Axial pressing.- Kharkov: Universitetizdat, 1962.- 52 p.
II. Extrinsic pressure.- Kharkov: Universitetizdat,1962.-62 p.
III.Torsion.- Kharkov: Universitetizdat, 1962.- 72 p.
IV. Limitarily elastic shells.-Kharkov: Universitetizdat,1963. - 92 p.
11. Strictly convex shells under postcritical deformations(in Russian):
I. Spherical shells.- Kharkov: Universitetizdat, 1965.- 91 p.
II. Loss of stability of shells.- Kharkov: Universitetizdat, 1965.- 79 p.
12. Geometric theory of stability of shells (in Russian).- Moscow: Nauka, 1966.- 296 p.
13. Geometrical methods in non-linear theory of elastic shells (in Russian).- Moscow: Nauka, 1967.- 280 p.
14. Extrinsic geometry of convex surfaces(in English).-Providence, R.I., AMS, 1973.- 665 p.
15. Elementary geometry: planimetry (in Russian).- Moscow: Nauka, 1969.- 127 p.
16. Elementary geometry: stereometry (in Russian).- Moscow: Nauka, 1970.- 100 p.
17. Geometria elemental (in Spanish).-Moscow: Mir Publishers,1974, 224 p.
18. Hilbert`s fourth problem (in English).- Washington: Scripta, 1979.- 97 p.
19. The Minkowsky multidimensional problem (in English).- Washington: Scripta, 1979.- 97 p.
20. Bending of surfaces and stability of shells (in English).- Providence, R.I.: AMS, 1989.- 77 p.
21. Multidimensional Monge-Ampere equation (in English). Rev. in Math.&Math.Phys., 1995, v. 10., p. 1-103.
A.V. Pogorelov's textbooks
22. Lectures on differential geometry (in English).- Groningen, P. Noordhoff, 1957.- 172 p.; 2nd ed. 1967.
23. Lectures on analytic geometry (in Russian).- Kharkov : Universitetizdat, 1957.- 162 p.; 2nd ed. 1963.
24. Lectures on the foundations of geometry (in English).- Groningen, P. Noordhoff, 1966.- 137 p.
25. Analytical geometry (in Russian).- Moscow: Nauka,1968.-176 p.; 2nd ed. 1978.
26. Differential geometry (in Russian).- Moscow: Nauka, 1969.- 176 p; 2nd ed. 1979.
27. Foundations of geometry (in Russian).- Moscow: Nauka, 1969.- 152 p.; 2nd ed. 1979.
28. Geometry (in Russian).- Manual for teachers.- Moscow: Prosveschenie, 1979.- 176 p.
29. Geometry (in Russian).- Experimental text-book for comprehensive school.- Kiev: Radjanska shkola, 1980.- 224 p.
30. Geometry 6-10 (in Russian).- Experimental text-book for secondary school.- Moscow: Prosveschenie, 1981.- 261 p.
31. Geometry 6-10 (in Russian).- Manual for secondary school.- Moscow: Prosveschenie, 1982.- 288 p.; 2nd - 8th eds. 1983 -1989.
32. Geometry (in English).- Manual for higher school, speciality "Mathematics".- Moscow: Mir Publishers, 1987.- 312 p.
33. Geometry 7-11 (in Russian).- Text-book for secondary school.- Moscow: Prosveschenie,1990.-384 p.; 2nd. - 5th eds. 1991-1995.
34. Geometry 7-9 (in Ukrainian).- Manual for secondary school.- Šiev: Osvita.- 1994.- 224 p.
35. Geometry 10-11 (in Ukrainian).- Manual for secondary school.- Kiev: Osvita.- 1994.- 128 p.